f64.rs

//! Constants specific to the `f64` double-precision floating point type.
//!
//! *[See also the `f64` primitive type][f64].*
//!
//! Mathematically significant numbers are provided in the `consts` sub-module.
//!
//! For the constants defined directly in this module
//! (as distinct from those defined in the `consts` sub-module),
//! new code should instead use the associated constants
//! defined directly on the `f64` type.

#![stable(feature = "rust1", since = "1.0.0")]

use crate::convert::FloatToInt;
#[cfg(not(test))]
use crate::intrinsics;
use crate::mem;
use crate::num::FpCategory;

/// The radix or base of the internal representation of `f64`.
/// Use [`f64::RADIX`] instead.
///
/// # Examples
///
/// ```rust
/// // deprecated way
/// # #[allow(deprecated, deprecated_in_future)]
/// let r = std::f64::RADIX;
///
/// // intended way
/// let r = f64::RADIX;
/// ```
#[stable(feature = "rust1", since = "1.0.0")]
#[rustc_deprecated(since = "TBD", reason = "replaced by the `RADIX` associated constant on `f64`")]
pub const RADIX: u32 = f64::RADIX;

/// Number of significant digits in base 2.
/// Use [`f64::MANTISSA_DIGITS`] instead.
///
/// # Examples
///
/// ```rust
/// // deprecated way
/// # #[allow(deprecated, deprecated_in_future)]
/// let d = std::f64::MANTISSA_DIGITS;
///
/// // intended way
/// let d = f64::MANTISSA_DIGITS;
/// ```
#[stable(feature = "rust1", since = "1.0.0")]
#[rustc_deprecated(
    since = "TBD",
    reason = "replaced by the `MANTISSA_DIGITS` associated constant on `f64`"
)]
pub const MANTISSA_DIGITS: u32 = f64::MANTISSA_DIGITS;

/// Approximate number of significant digits in base 10.
/// Use [`f64::DIGITS`] instead.
///
/// # Examples
///
/// ```rust
/// // deprecated way
/// # #[allow(deprecated, deprecated_in_future)]
/// let d = std::f64::DIGITS;
///
/// // intended way
/// let d = f64::DIGITS;
/// ```
#[stable(feature = "rust1", since = "1.0.0")]
#[rustc_deprecated(since = "TBD", reason = "replaced by the `DIGITS` associated constant on `f64`")]
pub const DIGITS: u32 = f64::DIGITS;

/// [Machine epsilon] value for `f64`.
/// Use [`f64::EPSILON`] instead.
///
/// This is the difference between `1.0` and the next larger representable number.
///
/// [Machine epsilon]: https://en.wikipedia.org/wiki/Machine_epsilon
///
/// # Examples
///
/// ```rust
/// // deprecated way
/// # #[allow(deprecated, deprecated_in_future)]
/// let e = std::f64::EPSILON;
///
/// // intended way
/// let e = f64::EPSILON;
/// ```
#[stable(feature = "rust1", since = "1.0.0")]
#[rustc_deprecated(
    since = "TBD",
    reason = "replaced by the `EPSILON` associated constant on `f64`"
)]
pub const EPSILON: f64 = f64::EPSILON;

/// Smallest finite `f64` value.
/// Use [`f64::MIN`] instead.
///
/// # Examples
///
/// ```rust
/// // deprecated way
/// # #[allow(deprecated, deprecated_in_future)]
/// let min = std::f64::MIN;
///
/// // intended way
/// let min = f64::MIN;
/// ```
#[stable(feature = "rust1", since = "1.0.0")]
#[rustc_deprecated(since = "TBD", reason = "replaced by the `MIN` associated constant on `f64`")]
pub const MIN: f64 = f64::MIN;

/// Smallest positive normal `f64` value.
/// Use [`f64::MIN_POSITIVE`] instead.
///
/// # Examples
///
/// ```rust
/// // deprecated way
/// # #[allow(deprecated, deprecated_in_future)]
/// let min = std::f64::MIN_POSITIVE;
///
/// // intended way
/// let min = f64::MIN_POSITIVE;
/// ```
#[stable(feature = "rust1", since = "1.0.0")]
#[rustc_deprecated(
    since = "TBD",
    reason = "replaced by the `MIN_POSITIVE` associated constant on `f64`"
)]
pub const MIN_POSITIVE: f64 = f64::MIN_POSITIVE;

/// Largest finite `f64` value.
/// Use [`f64::MAX`] instead.
///
/// # Examples
///
/// ```rust
/// // deprecated way
/// # #[allow(deprecated, deprecated_in_future)]
/// let max = std::f64::MAX;
///
/// // intended way
/// let max = f64::MAX;
/// ```
#[stable(feature = "rust1", since = "1.0.0")]
#[rustc_deprecated(since = "TBD", reason = "replaced by the `MAX` associated constant on `f64`")]
pub const MAX: f64 = f64::MAX;

/// One greater than the minimum possible normal power of 2 exponent.
/// Use [`f64::MIN_EXP`] instead.
///
/// # Examples
///
/// ```rust
/// // deprecated way
/// # #[allow(deprecated, deprecated_in_future)]
/// let min = std::f64::MIN_EXP;
///
/// // intended way
/// let min = f64::MIN_EXP;
/// ```
#[stable(feature = "rust1", since = "1.0.0")]
#[rustc_deprecated(
    since = "TBD",
    reason = "replaced by the `MIN_EXP` associated constant on `f64`"
)]
pub const MIN_EXP: i32 = f64::MIN_EXP;

/// Maximum possible power of 2 exponent.
/// Use [`f64::MAX_EXP`] instead.
///
/// # Examples
///
/// ```rust
/// // deprecated way
/// # #[allow(deprecated, deprecated_in_future)]
/// let max = std::f64::MAX_EXP;
///
/// // intended way
/// let max = f64::MAX_EXP;
/// ```
#[stable(feature = "rust1", since = "1.0.0")]
#[rustc_deprecated(
    since = "TBD",
    reason = "replaced by the `MAX_EXP` associated constant on `f64`"
)]
pub const MAX_EXP: i32 = f64::MAX_EXP;

/// Minimum possible normal power of 10 exponent.
/// Use [`f64::MIN_10_EXP`] instead.
///
/// # Examples
///
/// ```rust
/// // deprecated way
/// # #[allow(deprecated, deprecated_in_future)]
/// let min = std::f64::MIN_10_EXP;
///
/// // intended way
/// let min = f64::MIN_10_EXP;
/// ```
#[stable(feature = "rust1", since = "1.0.0")]
#[rustc_deprecated(
    since = "TBD",
    reason = "replaced by the `MIN_10_EXP` associated constant on `f64`"
)]
pub const MIN_10_EXP: i32 = f64::MIN_10_EXP;

/// Maximum possible power of 10 exponent.
/// Use [`f64::MAX_10_EXP`] instead.
///
/// # Examples
///
/// ```rust
/// // deprecated way
/// # #[allow(deprecated, deprecated_in_future)]
/// let max = std::f64::MAX_10_EXP;
///
/// // intended way
/// let max = f64::MAX_10_EXP;
/// ```
#[stable(feature = "rust1", since = "1.0.0")]
#[rustc_deprecated(
    since = "TBD",
    reason = "replaced by the `MAX_10_EXP` associated constant on `f64`"
)]
pub const MAX_10_EXP: i32 = f64::MAX_10_EXP;

/// Not a Number (NaN).
/// Use [`f64::NAN`] instead.
///
/// # Examples
///
/// ```rust
/// // deprecated way
/// # #[allow(deprecated, deprecated_in_future)]
/// let nan = std::f64::NAN;
///
/// // intended way
/// let nan = f64::NAN;
/// ```
#[stable(feature = "rust1", since = "1.0.0")]
#[rustc_deprecated(since = "TBD", reason = "replaced by the `NAN` associated constant on `f64`")]
pub const NAN: f64 = f64::NAN;

/// Infinity (∞).
/// Use [`f64::INFINITY`] instead.
///
/// # Examples
///
/// ```rust
/// // deprecated way
/// # #[allow(deprecated, deprecated_in_future)]
/// let inf = std::f64::INFINITY;
///
/// // intended way
/// let inf = f64::INFINITY;
/// ```
#[stable(feature = "rust1", since = "1.0.0")]
#[rustc_deprecated(
    since = "TBD",
    reason = "replaced by the `INFINITY` associated constant on `f64`"
)]
pub const INFINITY: f64 = f64::INFINITY;

/// Negative infinity (−∞).
/// Use [`f64::NEG_INFINITY`] instead.
///
/// # Examples
///
/// ```rust
/// // deprecated way
/// # #[allow(deprecated, deprecated_in_future)]
/// let ninf = std::f64::NEG_INFINITY;
///
/// // intended way
/// let ninf = f64::NEG_INFINITY;
/// ```
#[stable(feature = "rust1", since = "1.0.0")]
#[rustc_deprecated(
    since = "TBD",
    reason = "replaced by the `NEG_INFINITY` associated constant on `f64`"
)]
pub const NEG_INFINITY: f64 = f64::NEG_INFINITY;

/// Basic mathematical constants.
#[stable(feature = "rust1", since = "1.0.0")]
pub mod consts {
    // FIXME: replace with mathematical constants from cmath.

    /// Archimedes' constant (π)
    #[stable(feature = "rust1", since = "1.0.0")]
    pub const PI: f64 = 3.14159265358979323846264338327950288_f64;

    /// The full circle constant (τ)
    ///
    /// Equal to 2π.
    #[stable(feature = "tau_constant", since = "1.47.0")]
    pub const TAU: f64 = 6.28318530717958647692528676655900577_f64;

    /// π/2
    #[stable(feature = "rust1", since = "1.0.0")]
    pub const FRAC_PI_2: f64 = 1.57079632679489661923132169163975144_f64;

    /// π/3
    #[stable(feature = "rust1", since = "1.0.0")]
    pub const FRAC_PI_3: f64 = 1.04719755119659774615421446109316763_f64;

    /// π/4
    #[stable(feature = "rust1", since = "1.0.0")]
    pub const FRAC_PI_4: f64 = 0.785398163397448309615660845819875721_f64;

    /// π/6
    #[stable(feature = "rust1", since = "1.0.0")]
    pub const FRAC_PI_6: f64 = 0.52359877559829887307710723054658381_f64;

    /// π/8
    #[stable(feature = "rust1", since = "1.0.0")]
    pub const FRAC_PI_8: f64 = 0.39269908169872415480783042290993786_f64;

    /// 1/π
    #[stable(feature = "rust1", since = "1.0.0")]
    pub const FRAC_1_PI: f64 = 0.318309886183790671537767526745028724_f64;

    /// 2/π
    #[stable(feature = "rust1", since = "1.0.0")]
    pub const FRAC_2_PI: f64 = 0.636619772367581343075535053490057448_f64;

    /// 2/sqrt(π)
    #[stable(feature = "rust1", since = "1.0.0")]
    pub const FRAC_2_SQRT_PI: f64 = 1.12837916709551257389615890312154517_f64;

    /// sqrt(2)
    #[stable(feature = "rust1", since = "1.0.0")]
    pub const SQRT_2: f64 = 1.41421356237309504880168872420969808_f64;

    /// 1/sqrt(2)
    #[stable(feature = "rust1", since = "1.0.0")]
    pub const FRAC_1_SQRT_2: f64 = 0.707106781186547524400844362104849039_f64;

    /// Euler's number (e)
    #[stable(feature = "rust1", since = "1.0.0")]
    pub const E: f64 = 2.71828182845904523536028747135266250_f64;

    /// log<sub>2</sub>(10)
    #[stable(feature = "extra_log_consts", since = "1.43.0")]
    pub const LOG2_10: f64 = 3.32192809488736234787031942948939018_f64;

    /// log<sub>2</sub>(e)
    #[stable(feature = "rust1", since = "1.0.0")]
    pub const LOG2_E: f64 = 1.44269504088896340735992468100189214_f64;

    /// log<sub>10</sub>(2)
    #[stable(feature = "extra_log_consts", since = "1.43.0")]
    pub const LOG10_2: f64 = 0.301029995663981195213738894724493027_f64;

    /// log<sub>10</sub>(e)
    #[stable(feature = "rust1", since = "1.0.0")]
    pub const LOG10_E: f64 = 0.434294481903251827651128918916605082_f64;

    /// ln(2)
    #[stable(feature = "rust1", since = "1.0.0")]
    pub const LN_2: f64 = 0.693147180559945309417232121458176568_f64;

    /// ln(10)
    #[stable(feature = "rust1", since = "1.0.0")]
    pub const LN_10: f64 = 2.30258509299404568401799145468436421_f64;
}

#[lang = "f64"]
#[cfg(not(test))]
impl f64 {
    /// The radix or base of the internal representation of `f64`.
    #[stable(feature = "assoc_int_consts", since = "1.43.0")]
    pub const RADIX: u32 = 2;

    /// Number of significant digits in base 2.
    #[stable(feature = "assoc_int_consts", since = "1.43.0")]
    pub const MANTISSA_DIGITS: u32 = 53;
    /// Approximate number of significant digits in base 10.
    #[stable(feature = "assoc_int_consts", since = "1.43.0")]
    pub const DIGITS: u32 = 15;

    /// [Machine epsilon] value for `f64`.
    ///
    /// This is the difference between `1.0` and the next larger representable number.
    ///
    /// [Machine epsilon]: https://en.wikipedia.org/wiki/Machine_epsilon
    #[stable(feature = "assoc_int_consts", since = "1.43.0")]
    pub const EPSILON: f64 = 2.2204460492503131e-16_f64;

    /// Smallest finite `f64` value.
    #[stable(feature = "assoc_int_consts", since = "1.43.0")]
    pub const MIN: f64 = -1.7976931348623157e+308_f64;
    /// Smallest positive normal `f64` value.
    #[stable(feature = "assoc_int_consts", since = "1.43.0")]
    pub const MIN_POSITIVE: f64 = 2.2250738585072014e-308_f64;
    /// Largest finite `f64` value.
    #[stable(feature = "assoc_int_consts", since = "1.43.0")]
    pub const MAX: f64 = 1.7976931348623157e+308_f64;

    /// One greater than the minimum possible normal power of 2 exponent.
    #[stable(feature = "assoc_int_consts", since = "1.43.0")]
    pub const MIN_EXP: i32 = -1021;
    /// Maximum possible power of 2 exponent.
    #[stable(feature = "assoc_int_consts", since = "1.43.0")]
    pub const MAX_EXP: i32 = 1024;

    /// Minimum possible normal power of 10 exponent.
    #[stable(feature = "assoc_int_consts", since = "1.43.0")]
    pub const MIN_10_EXP: i32 = -307;
    /// Maximum possible power of 10 exponent.
    #[stable(feature = "assoc_int_consts", since = "1.43.0")]
    pub const MAX_10_EXP: i32 = 308;

    /// Not a Number (NaN).
    #[stable(feature = "assoc_int_consts", since = "1.43.0")]
    pub const NAN: f64 = 0.0_f64 / 0.0_f64;
    /// Infinity (∞).
    #[stable(feature = "assoc_int_consts", since = "1.43.0")]
    pub const INFINITY: f64 = 1.0_f64 / 0.0_f64;
    /// Negative infinity (−∞).
    #[stable(feature = "assoc_int_consts", since = "1.43.0")]
    pub const NEG_INFINITY: f64 = -1.0_f64 / 0.0_f64;

    /// Returns `true` if this value is `NaN`.
    ///
    /// ```
    /// let nan = f64::NAN;
    /// let f = 7.0_f64;
    ///
    /// assert!(nan.is_nan());
    /// assert!(!f.is_nan());
    /// ```
    #[must_use]
    #[stable(feature = "rust1", since = "1.0.0")]
    #[rustc_const_unstable(feature = "const_float_classify", issue = "72505")]
    #[inline]
    pub const fn is_nan(self) -> bool {
        self != self
    }

    // FIXME(#50145): `abs` is publicly unavailable in libcore due to
    // concerns about portability, so this implementation is for
    // private use internally.
    #[inline]
    #[rustc_const_unstable(feature = "const_float_classify", issue = "72505")]
    pub(crate) const fn abs_private(self) -> f64 {
        f64::from_bits(self.to_bits() & 0x7fff_ffff_ffff_ffff)
    }

    /// Returns `true` if this value is positive infinity or negative infinity, and
    /// `false` otherwise.
    ///
    /// ```
    /// let f = 7.0f64;
    /// let inf = f64::INFINITY;
    /// let neg_inf = f64::NEG_INFINITY;
    /// let nan = f64::NAN;
    ///
    /// assert!(!f.is_infinite());
    /// assert!(!nan.is_infinite());
    ///
    /// assert!(inf.is_infinite());
    /// assert!(neg_inf.is_infinite());
    /// ```
    #[must_use]
    #[stable(feature = "rust1", since = "1.0.0")]
    #[rustc_const_unstable(feature = "const_float_classify", issue = "72505")]
    #[inline]
    pub const fn is_infinite(self) -> bool {
        self.abs_private() == Self::INFINITY
    }

    /// Returns `true` if this number is neither infinite nor `NaN`.
    ///
    /// ```
    /// let f = 7.0f64;
    /// let inf: f64 = f64::INFINITY;
    /// let neg_inf: f64 = f64::NEG_INFINITY;
    /// let nan: f64 = f64::NAN;
    ///
    /// assert!(f.is_finite());
    ///
    /// assert!(!nan.is_finite());
    /// assert!(!inf.is_finite());
    /// assert!(!neg_inf.is_finite());
    /// ```
    #[must_use]
    #[stable(feature = "rust1", since = "1.0.0")]
    #[rustc_const_unstable(feature = "const_float_classify", issue = "72505")]
    #[inline]
    pub const fn is_finite(self) -> bool {
        // There's no need to handle NaN separately: if self is NaN,
        // the comparison is not true, exactly as desired.
        self.abs_private() < Self::INFINITY
    }

    /// Returns `true` if the number is [subnormal].
    ///
    /// ```
    /// let min = f64::MIN_POSITIVE; // 2.2250738585072014e-308_f64
    /// let max = f64::MAX;
    /// let lower_than_min = 1.0e-308_f64;
    /// let zero = 0.0_f64;
    ///
    /// assert!(!min.is_subnormal());
    /// assert!(!max.is_subnormal());
    ///
    /// assert!(!zero.is_subnormal());
    /// assert!(!f64::NAN.is_subnormal());
    /// assert!(!f64::INFINITY.is_subnormal());
    /// // Values between `0` and `min` are Subnormal.
    /// assert!(lower_than_min.is_subnormal());
    /// ```
    /// [subnormal]: https://en.wikipedia.org/wiki/Denormal_number
    #[must_use]
    #[stable(feature = "is_subnormal", since = "1.53.0")]
    #[rustc_const_unstable(feature = "const_float_classify", issue = "72505")]
    #[inline]
    pub const fn is_subnormal(self) -> bool {
        matches!(self.classify(), FpCategory::Subnormal)
    }

    /// Returns `true` if the number is neither zero, infinite,
    /// [subnormal], or `NaN`.
    ///
    /// ```
    /// let min = f64::MIN_POSITIVE; // 2.2250738585072014e-308f64
    /// let max = f64::MAX;
    /// let lower_than_min = 1.0e-308_f64;
    /// let zero = 0.0f64;
    ///
    /// assert!(min.is_normal());
    /// assert!(max.is_normal());
    ///
    /// assert!(!zero.is_normal());
    /// assert!(!f64::NAN.is_normal());
    /// assert!(!f64::INFINITY.is_normal());
    /// // Values between `0` and `min` are Subnormal.
    /// assert!(!lower_than_min.is_normal());
    /// ```
    /// [subnormal]: https://en.wikipedia.org/wiki/Denormal_number
    #[must_use]
    #[stable(feature = "rust1", since = "1.0.0")]
    #[rustc_const_unstable(feature = "const_float_classify", issue = "72505")]
    #[inline]
    pub const fn is_normal(self) -> bool {
        matches!(self.classify(), FpCategory::Normal)
    }

    /// Returns the floating point category of the number. If only one property
    /// is going to be tested, it is generally faster to use the specific
    /// predicate instead.
    ///
    /// ```
    /// use std::num::FpCategory;
    ///
    /// let num = 12.4_f64;
    /// let inf = f64::INFINITY;
    ///
    /// assert_eq!(num.classify(), FpCategory::Normal);
    /// assert_eq!(inf.classify(), FpCategory::Infinite);
    /// ```
    #[stable(feature = "rust1", since = "1.0.0")]
    #[rustc_const_unstable(feature = "const_float_classify", issue = "72505")]
    pub const fn classify(self) -> FpCategory {
        const EXP_MASK: u64 = 0x7ff0000000000000;
        const MAN_MASK: u64 = 0x000fffffffffffff;

        let bits = self.to_bits();
        match (bits & MAN_MASK, bits & EXP_MASK) {
            (0, 0) => FpCategory::Zero,
            (_, 0) => FpCategory::Subnormal,
            (0, EXP_MASK) => FpCategory::Infinite,
            (_, EXP_MASK) => FpCategory::Nan,
            _ => FpCategory::Normal,
        }
    }

    /// Returns `true` if `self` has a positive sign, including `+0.0`, `NaN`s with
    /// positive sign bit and positive infinity.
    ///
    /// ```
    /// let f = 7.0_f64;
    /// let g = -7.0_f64;
    ///
    /// assert!(f.is_sign_positive());
    /// assert!(!g.is_sign_positive());
    /// ```
    #[must_use]
    #[stable(feature = "rust1", since = "1.0.0")]
    #[rustc_const_unstable(feature = "const_float_classify", issue = "72505")]
    #[inline]
    pub const fn is_sign_positive(self) -> bool {
        !self.is_sign_negative()
    }

    #[must_use]
    #[stable(feature = "rust1", since = "1.0.0")]
    #[rustc_deprecated(since = "1.0.0", reason = "renamed to is_sign_positive")]
    #[inline]
    #[doc(hidden)]
    pub fn is_positive(self) -> bool {
        self.is_sign_positive()
    }

    /// Returns `true` if `self` has a negative sign, including `-0.0`, `NaN`s with
    /// negative sign bit and negative infinity.
    ///
    /// ```
    /// let f = 7.0_f64;
    /// let g = -7.0_f64;
    ///
    /// assert!(!f.is_sign_negative());
    /// assert!(g.is_sign_negative());
    /// ```
    #[must_use]
    #[stable(feature = "rust1", since = "1.0.0")]
    #[rustc_const_unstable(feature = "const_float_classify", issue = "72505")]
    #[inline]
    pub const fn is_sign_negative(self) -> bool {
        self.to_bits() & 0x8000_0000_0000_0000 != 0
    }

    #[must_use]
    #[stable(feature = "rust1", since = "1.0.0")]
    #[rustc_deprecated(since = "1.0.0", reason = "renamed to is_sign_negative")]
    #[inline]
    #[doc(hidden)]
    pub fn is_negative(self) -> bool {
        self.is_sign_negative()
    }

    /// Returns the least number greater than `self`.
    ///
    /// Let `TINY` be the smallest representable positive `f64`. Then,
    ///  - if `self.is_nan()`, this returns `self`;
    ///  - if `self` is [`NEG_INFINITY`], this returns [`MIN`];
    ///  - if `self` is `-TINY`, this returns -0.0;
    ///  - if `self` is -0.0 or +0.0, this returns `TINY`;
    ///  - if `self` is [`MAX`] or [`INFINITY`], this returns [`INFINITY`];
    ///  - otherwise the unique least value greater than `self` is returned.
    ///
    /// The identity `x.next_up() == -(-x).next_down()` holds for all `x`. When `x`
    /// is finite `x == x.next_up().next_down()` also holds.
    ///
    /// ```rust
    /// #![feature(float_next_up_down)]
    /// // f64::EPSILON is the difference between 1.0 and the next number up.
    /// assert_eq!(1.0f64.next_up(), 1.0 + f64::EPSILON);
    /// // But not for most numbers.
    /// assert!(0.1f64.next_up() < 0.1 + f64::EPSILON);
    /// assert_eq!(9007199254740992f64.next_up(), 9007199254740994.0);
    /// ```
    ///
    /// [`NEG_INFINITY`]: Self::NEG_INFINITY
    /// [`INFINITY`]: Self::INFINITY
    /// [`MIN`]: Self::MIN
    /// [`MAX`]: Self::MAX
    #[unstable(feature = "float_next_up_down", issue = "91399")]
    #[rustc_const_unstable(feature = "float_next_up_down", issue = "91399")]
    pub const fn next_up(self) -> Self {
        // We must use strictly integer arithmetic to prevent denormals from
        // flushing to zero after an arithmetic operation on some platforms.
        const TINY_BITS: u64 = 0x1; // Smallest positive f64.
        const CLEAR_SIGN_MASK: u64 = 0x7fff_ffff_ffff_ffff;

        let bits = self.to_bits();
        if self.is_nan() || bits == Self::INFINITY.to_bits() {
            return self;
        }

        let abs = bits & CLEAR_SIGN_MASK;
        let next_bits = if abs == 0 {
            TINY_BITS
        } else if bits == abs {
            bits + 1
        } else {
            bits - 1
        };
        Self::from_bits(next_bits)
    }

    /// Returns the greatest number less than `self`.
    ///
    /// Let `TINY` be the smallest representable positive `f64`. Then,
    ///  - if `self.is_nan()`, this returns `self`;
    ///  - if `self` is [`INFINITY`], this returns [`MAX`];
    ///  - if `self` is `TINY`, this returns 0.0;
    ///  - if `self` is -0.0 or +0.0, this returns `-TINY`;
    ///  - if `self` is [`MIN`] or [`NEG_INFINITY`], this returns [`NEG_INFINITY`];
    ///  - otherwise the unique greatest value less than `self` is returned.
    ///
    /// The identity `x.next_down() == -(-x).next_up()` holds for all `x`. When `x`
    /// is finite `x == x.next_down().next_up()` also holds.
    ///
    /// ```rust
    /// #![feature(float_next_up_down)]
    /// let x = 1.0f64;
    /// // Clamp value into range [0, 1).
    /// let clamped = x.clamp(0.0, 1.0f64.next_down());
    /// assert!(clamped < 1.0);
    /// assert_eq!(clamped.next_up(), 1.0);
    /// ```
    ///
    /// [`NEG_INFINITY`]: Self::NEG_INFINITY
    /// [`INFINITY`]: Self::INFINITY
    /// [`MIN`]: Self::MIN
    /// [`MAX`]: Self::MAX
    #[unstable(feature = "float_next_up_down", issue = "91399")]
    #[rustc_const_unstable(feature = "float_next_up_down", issue = "91399")]
    pub const fn next_down(self) -> Self {
        // We must use strictly integer arithmetic to prevent denormals from
        // flushing to zero after an arithmetic operation on some platforms.
        const NEG_TINY_BITS: u64 = 0x8000_0000_0000_0001; // Smallest (in magnitude) negative f64.
        const CLEAR_SIGN_MASK: u64 = 0x7fff_ffff_ffff_ffff;

        let bits = self.to_bits();
        if self.is_nan() || bits == Self::NEG_INFINITY.to_bits() {
            return self;
        }

        let abs = bits & CLEAR_SIGN_MASK;
        let next_bits = if abs == 0 {
            NEG_TINY_BITS
        } else if bits == abs {
            bits - 1
        } else {
            bits + 1
        };
        Self::from_bits(next_bits)
    }

    /// Takes the reciprocal (inverse) of a number, `1/x`.
    ///
    /// ```
    /// let x = 2.0_f64;
    /// let abs_difference = (x.recip() - (1.0 / x)).abs();
    ///
    /// assert!(abs_difference < 1e-10);
    /// ```
    #[stable(feature = "rust1", since = "1.0.0")]
    #[inline]
    pub fn recip(self) -> f64 {
        1.0 / self
    }

    /// Converts radians to degrees.
    ///
    /// ```
    /// let angle = std::f64::consts::PI;
    ///
    /// let abs_difference = (angle.to_degrees() - 180.0).abs();
    ///
    /// assert!(abs_difference < 1e-10);
    /// ```
    #[must_use = "this returns the result of the operation, \
                  without modifying the original"]
    #[stable(feature = "rust1", since = "1.0.0")]
    #[inline]
    pub fn to_degrees(self) -> f64 {
        // The division here is correctly rounded with respect to the true
        // value of 180/π. (This differs from f32, where a constant must be
        // used to ensure a correctly rounded result.)
        self * (180.0f64 / consts::PI)
    }

    /// Converts degrees to radians.
    ///
    /// ```
    /// let angle = 180.0_f64;
    ///
    /// let abs_difference = (angle.to_radians() - std::f64::consts::PI).abs();
    ///
    /// assert!(abs_difference < 1e-10);
    /// ```
    #[must_use = "this returns the result of the operation, \
                  without modifying the original"]
    #[stable(feature = "rust1", since = "1.0.0")]
    #[inline]
    pub fn to_radians(self) -> f64 {
        let value: f64 = consts::PI;
        self * (value / 180.0)
    }

    /// Returns the maximum of the two numbers.
    ///
    /// ```
    /// let x = 1.0_f64;
    /// let y = 2.0_f64;
    ///
    /// assert_eq!(x.max(y), y);
    /// ```
    ///
    /// If one of the arguments is NaN, then the other argument is returned.
    #[stable(feature = "rust1", since = "1.0.0")]
    #[inline]
    pub fn max(self, other: f64) -> f64 {
        intrinsics::maxnumf64(self, other)
    }

    /// Returns the minimum of the two numbers.
    ///
    /// ```
    /// let x = 1.0_f64;
    /// let y = 2.0_f64;
    ///
    /// assert_eq!(x.min(y), x);
    /// ```
    ///
    /// If one of the arguments is NaN, then the other argument is returned.
    #[stable(feature = "rust1", since = "1.0.0")]
    #[inline]
    pub fn min(self, other: f64) -> f64 {
        intrinsics::minnumf64(self, other)
    }

    /// Rounds toward zero and converts to any primitive integer type,
    /// assuming that the value is finite and fits in that type.
    ///
    /// ```
    /// let value = 4.6_f64;
    /// let rounded = unsafe { value.to_int_unchecked::<u16>() };
    /// assert_eq!(rounded, 4);
    ///
    /// let value = -128.9_f64;
    /// let rounded = unsafe { value.to_int_unchecked::<i8>() };
    /// assert_eq!(rounded, i8::MIN);
    /// ```
    ///
    /// # Safety
    ///
    /// The value must:
    ///
    /// * Not be `NaN`
    /// * Not be infinite
    /// * Be representable in the return type `Int`, after truncating off its fractional part
    #[must_use = "this returns the result of the operation, \
                  without modifying the original"]
    #[stable(feature = "float_approx_unchecked_to", since = "1.44.0")]
    #[inline]
    pub unsafe fn to_int_unchecked<Int>(self) -> Int
    where
        Self: FloatToInt<Int>,
    {
        // SAFETY: the caller must uphold the safety contract for
        // `FloatToInt::to_int_unchecked`.
        unsafe { FloatToInt::<Int>::to_int_unchecked(self) }
    }

    /// Raw transmutation to `u64`.
    ///
    /// This is currently identical to `transmute::<f64, u64>(self)` on all platforms.
    ///
    /// See [`from_bits`](Self::from_bits) for some discussion of the
    /// portability of this operation (there are almost no issues).
    ///
    /// Note that this function is distinct from `as` casting, which attempts to
    /// preserve the *numeric* value, and not the bitwise value.
    ///
    /// # Examples
    ///
    /// ```
    /// assert!((1f64).to_bits() != 1f64 as u64); // to_bits() is not casting!
    /// assert_eq!((12.5f64).to_bits(), 0x4029000000000000);
    ///
    /// ```
    #[must_use = "this returns the result of the operation, \
                  without modifying the original"]
    #[stable(feature = "float_bits_conv", since = "1.20.0")]
    #[rustc_const_unstable(feature = "const_float_bits_conv", issue = "72447")]
    #[inline]
    pub const fn to_bits(self) -> u64 {
        // SAFETY: `u64` is a plain old datatype so we can always transmute to it
        unsafe { mem::transmute(self) }
    }

    /// Raw transmutation from `u64`.
    ///
    /// This is currently identical to `transmute::<u64, f64>(v)` on all platforms.
    /// It turns out this is incredibly portable, for two reasons:
    ///
    /// * Floats and Ints have the same endianness on all supported platforms.
    /// * IEEE-754 very precisely specifies the bit layout of floats.
    ///
    /// However there is one caveat: prior to the 2008 version of IEEE-754, how
    /// to interpret the NaN signaling bit wasn't actually specified. Most platforms
    /// (notably x86 and ARM) picked the interpretation that was ultimately
    /// standardized in 2008, but some didn't (notably MIPS). As a result, all
    /// signaling NaNs on MIPS are quiet NaNs on x86, and vice-versa.
    ///
    /// Rather than trying to preserve signaling-ness cross-platform, this
    /// implementation favors preserving the exact bits. This means that
    /// any payloads encoded in NaNs will be preserved even if the result of
    /// this method is sent over the network from an x86 machine to a MIPS one.
    ///
    /// If the results of this method are only manipulated by the same
    /// architecture that produced them, then there is no portability concern.
    ///
    /// If the input isn't NaN, then there is no portability concern.
    ///
    /// If you don't care about signaling-ness (very likely), then there is no
    /// portability concern.
    ///
    /// Note that this function is distinct from `as` casting, which attempts to
    /// preserve the *numeric* value, and not the bitwise value.
    ///
    /// # Examples
    ///
    /// ```
    /// let v = f64::from_bits(0x4029000000000000);
    /// assert_eq!(v, 12.5);
    /// ```
    #[stable(feature = "float_bits_conv", since = "1.20.0")]
    #[rustc_const_unstable(feature = "const_float_bits_conv", issue = "72447")]
    #[must_use]
    #[inline]
    pub const fn from_bits(v: u64) -> Self {
        // SAFETY: `u64` is a plain old datatype so we can always transmute from it
        // It turns out the safety issues with sNaN were overblown! Hooray!
        unsafe { mem::transmute(v) }
    }

    /// Return the memory representation of this floating point number as a byte array in
    /// big-endian (network) byte order.
    ///
    /// # Examples
    ///
    /// ```
    /// let bytes = 12.5f64.to_be_bytes();
    /// assert_eq!(bytes, [0x40, 0x29, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00]);
    /// ```
    #[must_use = "this returns the result of the operation, \
                  without modifying the original"]
    #[stable(feature = "float_to_from_bytes", since = "1.40.0")]
    #[rustc_const_unstable(feature = "const_float_bits_conv", issue = "72447")]
    #[inline]
    pub const fn to_be_bytes(self) -> [u8; 8] {
        self.to_bits().to_be_bytes()
    }

    /// Return the memory representation of this floating point number as a byte array in
    /// little-endian byte order.
    ///
    /// # Examples
    ///
    /// ```
    /// let bytes = 12.5f64.to_le_bytes();
    /// assert_eq!(bytes, [0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x29, 0x40]);
    /// ```
    #[must_use = "this returns the result of the operation, \
                  without modifying the original"]
    #[stable(feature = "float_to_from_bytes", since = "1.40.0")]
    #[rustc_const_unstable(feature = "const_float_bits_conv", issue = "72447")]
    #[inline]
    pub const fn to_le_bytes(self) -> [u8; 8] {
        self.to_bits().to_le_bytes()
    }

    /// Return the memory representation of this floating point number as a byte array in
    /// native byte order.
    ///
    /// As the target platform's native endianness is used, portable code
    /// should use [`to_be_bytes`] or [`to_le_bytes`], as appropriate, instead.
    ///
    /// [`to_be_bytes`]: f64::to_be_bytes
    /// [`to_le_bytes`]: f64::to_le_bytes
    ///
    /// # Examples
    ///
    /// ```
    /// let bytes = 12.5f64.to_ne_bytes();
    /// assert_eq!(
    ///     bytes,
    ///     if cfg!(target_endian = "big") {
    ///         [0x40, 0x29, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00]
    ///     } else {
    ///         [0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x29, 0x40]
    ///     }
    /// );
    /// ```
    #[must_use = "this returns the result of the operation, \
                  without modifying the original"]
    #[stable(feature = "float_to_from_bytes", since = "1.40.0")]
    #[rustc_const_unstable(feature = "const_float_bits_conv", issue = "72447")]
    #[inline]
    pub const fn to_ne_bytes(self) -> [u8; 8] {
        self.to_bits().to_ne_bytes()
    }

    /// Create a floating point value from its representation as a byte array in big endian.
    ///
    /// # Examples
    ///
    /// ```
    /// let value = f64::from_be_bytes([0x40, 0x29, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00]);
    /// assert_eq!(value, 12.5);
    /// ```
    #[stable(feature = "float_to_from_bytes", since = "1.40.0")]
    #[rustc_const_unstable(feature = "const_float_bits_conv", issue = "72447")]
    #[must_use]
    #[inline]
    pub const fn from_be_bytes(bytes: [u8; 8]) -> Self {
        Self::from_bits(u64::from_be_bytes(bytes))
    }

    /// Create a floating point value from its representation as a byte array in little endian.
    ///
    /// # Examples
    ///
    /// ```
    /// let value = f64::from_le_bytes([0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x29, 0x40]);
    /// assert_eq!(value, 12.5);
    /// ```
    #[stable(feature = "float_to_from_bytes", since = "1.40.0")]
    #[rustc_const_unstable(feature = "const_float_bits_conv", issue = "72447")]
    #[must_use]
    #[inline]
    pub const fn from_le_bytes(bytes: [u8; 8]) -> Self {
        Self::from_bits(u64::from_le_bytes(bytes))
    }

    /// Create a floating point value from its representation as a byte array in native endian.
    ///
    /// As the target platform's native endianness is used, portable code
    /// likely wants to use [`from_be_bytes`] or [`from_le_bytes`], as
    /// appropriate instead.
    ///
    /// [`from_be_bytes`]: f64::from_be_bytes
    /// [`from_le_bytes`]: f64::from_le_bytes
    ///
    /// # Examples
    ///
    /// ```
    /// let value = f64::from_ne_bytes(if cfg!(target_endian = "big") {
    ///     [0x40, 0x29, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00]
    /// } else {
    ///     [0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x29, 0x40]
    /// });
    /// assert_eq!(value, 12.5);
    /// ```
    #[stable(feature = "float_to_from_bytes", since = "1.40.0")]
    #[rustc_const_unstable(feature = "const_float_bits_conv", issue = "72447")]
    #[must_use]
    #[inline]
    pub const fn from_ne_bytes(bytes: [u8; 8]) -> Self {
        Self::from_bits(u64::from_ne_bytes(bytes))
    }

    /// Returns an ordering between self and other values.
    /// Unlike the standard partial comparison between floating point numbers,
    /// this comparison always produces an ordering in accordance to
    /// the totalOrder predicate as defined in IEEE 754 (2008 revision)
    /// floating point standard. The values are ordered in following order:
    /// - Negative quiet NaN
    /// - Negative signaling NaN
    /// - Negative infinity
    /// - Negative numbers
    /// - Negative subnormal numbers
    /// - Negative zero
    /// - Positive zero
    /// - Positive subnormal numbers
    /// - Positive numbers
    /// - Positive infinity
    /// - Positive signaling NaN
    /// - Positive quiet NaN
    ///
    /// Note that this function does not always agree with the [`PartialOrd`]
    /// and [`PartialEq`] implementations of `f64`. In particular, they regard
    /// negative and positive zero as equal, while `total_cmp` doesn't.
    ///
    /// # Example
    /// ```
    /// #![feature(total_cmp)]
    /// struct GoodBoy {
    ///     name: String,
    ///     weight: f64,
    /// }
    ///
    /// let mut bois = vec![
    ///     GoodBoy { name: "Pucci".to_owned(), weight: 0.1 },
    ///     GoodBoy { name: "Woofer".to_owned(), weight: 99.0 },
    ///     GoodBoy { name: "Yapper".to_owned(), weight: 10.0 },
    ///     GoodBoy { name: "Chonk".to_owned(), weight: f64::INFINITY },
    ///     GoodBoy { name: "Abs. Unit".to_owned(), weight: f64::NAN },
    ///     GoodBoy { name: "Floaty".to_owned(), weight: -5.0 },
    /// ];
    ///
    /// bois.sort_by(|a, b| a.weight.total_cmp(&b.weight));
    /// # assert!(bois.into_iter().map(|b| b.weight)
    /// #     .zip([-5.0, 0.1, 10.0, 99.0, f64::INFINITY, f64::NAN].iter())
    /// #     .all(|(a, b)| a.to_bits() == b.to_bits()))
    /// ```
    #[unstable(feature = "total_cmp", issue = "72599")]
    #[inline]
    pub fn total_cmp(&self, other: &Self) -> crate::cmp::Ordering {
        let mut left = self.to_bits() as i64;
        let mut right = other.to_bits() as i64;

        // In case of negatives, flip all the bits except the sign
        // to achieve a similar layout as two's complement integers
        //
        // Why does this work? IEEE 754 floats consist of three fields:
        // Sign bit, exponent and mantissa. The set of exponent and mantissa
        // fields as a whole have the property that their bitwise order is
        // equal to the numeric magnitude where the magnitude is defined.
        // The magnitude is not normally defined on NaN values, but
        // IEEE 754 totalOrder defines the NaN values also to follow the
        // bitwise order. This leads to order explained in the doc comment.
        // However, the representation of magnitude is the same for negative
        // and positive numbers – only the sign bit is different.
        // To easily compare the floats as signed integers, we need to
        // flip the exponent and mantissa bits in case of negative numbers.
        // We effectively convert the numbers to "two's complement" form.
        //
        // To do the flipping, we construct a mask and XOR against it.
        // We branchlessly calculate an "all-ones except for the sign bit"
        // mask from negative-signed values: right shifting sign-extends
        // the integer, so we "fill" the mask with sign bits, and then
        // convert to unsigned to push one more zero bit.
        // On positive values, the mask is all zeros, so it's a no-op.
        left ^= (((left >> 63) as u64) >> 1) as i64;
        right ^= (((right >> 63) as u64) >> 1) as i64;

        left.cmp(&right)
    }

    /// Restrict a value to a certain interval unless it is NaN.
    ///
    /// Returns `max` if `self` is greater than `max`, and `min` if `self` is
    /// less than `min`. Otherwise this returns `self`.
    ///
    /// Note that this function returns NaN if the initial value was NaN as
    /// well.
    ///
    /// # Panics
    ///
    /// Panics if `min > max`, `min` is NaN, or `max` is NaN.
    ///
    /// # Examples
    ///
    /// ```
    /// assert!((-3.0f64).clamp(-2.0, 1.0) == -2.0);
    /// assert!((0.0f64).clamp(-2.0, 1.0) == 0.0);
    /// assert!((2.0f64).clamp(-2.0, 1.0) == 1.0);
    /// assert!((f64::NAN).clamp(-2.0, 1.0).is_nan());
    /// ```
    #[must_use = "method returns a new number and does not mutate the original value"]
    #[stable(feature = "clamp", since = "1.50.0")]
    #[inline]
    pub fn clamp(self, min: f64, max: f64) -> f64 {
        assert!(min <= max);
        let mut x = self;
        if x < min {
            x = min;
        }
        if x > max {
            x = max;
        }
        x
    }
}